A Graph-based Rank-reduced Interface Preconditioner for the Harmonic Linearized Navier-Stokes Equations

Abstract Many advanced prediction and analysis tools for hypersonic boundary layer transition---including resolvent and Input/Output (I/O) analysis---rely on solutions of the harmonic, linearized Navier-Stokes equations (H-LNSE), which produce ill-conditioned and highly non-normal discrete systems. To overcome these challenges, we present a graph-based, rank-reduced interface preconditioner (GRIP) for the iterative solution of the H-LNSE, combining ideas from domain decomposition and graph propagation into a single framework. GRIP demonstrates near-linear scaling with respect to both memory and CPU utilization; it is inherently parallel, memory-efficient, physics-informed, and scalable. In testing, we expose a cause of F-GMRES breakdown for hypersonic linear systems and other non-normal operators. GRIP is applied to two- and three-dimensional Mach 6 boundary layer flows over a flat plate, shedding light on the importance of three-dimensional effects in canonical flows. Additionally, GRIP is applied to three-dimensional Mach 6 flow over a cone with a highly swept fin. Analysis of the response at 247 kHz shows amplification of vortical waves along the strong inboard vortex as well as milder amplification along the weaker, outboard vortex.